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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Communication in Biomathematical Sciences Jambura Journal of Biomathematics (JJBM) Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Peter, Olumuyiwa James
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Deterministic Double Dose Vaccination Model of COVID-19 Transmission Dynamics - Optimal Control Strategies with Cost-Effectiveness Analysis Abidemi, Afeez; Fatmawati; Peter, Olumuyiwa James
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.1

Abstract

In this study, we propose a deterministic double dose vaccination model of COVID-19 transmission dynamics optimal control with cost-effectiveness analysis. It is imperative for decision-makers and the government to prioritize the application of preventive and control measures for COVID-19 based on efficiency and costbenefit analysis. This is pivotal in resource-constrained regions where the disease is endemic. Thus, this work is mainly devoted with the development and analysis of an optimal control for COVID-19 dynamics with five timevarying functions; first dose vaccination, second dose vaccination, personal protection, testing or screening, and treatment. The model is qualitatively analysed with the overall goal to minimize the spread of COVID-19 and the costs related to control implementation with the aid of optimal control theory. The effect of adopting each control intervention in each of the three distinct groups which are created by classifying all conceivable combinations of at least three control interventions is demonstrated through the numerical simulations of the optimality system. Using the average cost-effectiveness ratio and incremental cost-effectiveness ratio techniques, the most economical control intervention is determined for each group. The study reveals that when the resources are readily available, application of the strategy that combines optimal first dose vaccination, personal protection, screening or testing and treatment is as efficient as implementing all the five optimal control interventions simultaneously as they both avert the same number of infections. However, in resource-limited communities when joint implementation of only three interventions is possible, the strategy combining personal protection, testing or screening and treatment is strongly recommended. Out of all the intervention options being considered, this strategy is also affirmed to be the most cost-effective overall. Economic evaluation of the control intervention strategies further suggests that combination of first dose vaccination, second dose vaccination, testing or screening and treatment is the most cost-effective strategy when implementation of only four interventions is strictly allowed.
Numerical Solution of Fractional Order Differential Equations by Chebyshev Least Squares Approximation Method Adebisi, Ajimot F.; Uwaheren, Ohigweren A.; Oseni, Wasiu A.; Ishola, Christie Y.; Peter, Olumuyiwa James
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 1 April 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i1.31034

Abstract

In this paper, fractional differential equations (FDEs) are solved numerically using the least squares method (LSM). Shifted Chebyshev polynomials are used as the basis functions, and the results are compared with the exact solutions. Several numerical examples are presented to illustrate the theoretical results and are also compared with the outcomes obtained from other numerical methods. It is found that the results of the proposed approximate method converge rapidly to the exact solutions.
STABILITY ANALYSIS OF A MATHEMATICAL MODEL OF RABIES SPREAD WITH VACCINATION IN HUMAN AND DOG POPULATIONS, INCLUDING AWARE AND UNAWARE EXPOSED SUBPOPULATIONS Sahusilawane, Maria Engeline; Ilwaru, Venn Yan Ishak; Lesnussa, Yopi Andry; Beay, Lazarus Kalvein; Ojo, Mayowa Micheal; Permadi, Vynska Amalia; Peter, Olumuyiwa James
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp861-878

Abstract

Rabies is a zoonotic disease that causes progressive and fatal inflammation of the brain and spinal cord, which can be prevented by vaccination. This study aims to analyze the stability of a mathematical model of rabies disease spread with vaccination in human and dog populations in Maluku Province. The model uses a system of ordinary differential equations that separates the human population into six subpopulations (6 variables) and the dog population into three subpopulations (3 variables). The new variables are unaware subpopulations that we divide from aware subpopulations. The results showed that disease-free and endemic equilibrium points could be achieved, and the stability of these equilibrium points was analyzed using basic reproduction numbers Both disease-free and endemic equilibrium points are locally asymptotically stable. The Numerical simulations were also conducted to determine the characteristics of each subpopulation. This study was to provide better insight into controlling the spread of rabies in Maluku Province and it can be used as a reference in developing mathematical models for other infectious diseases.
Implementation of non-standard finite difference on a predator prey model considering cannibalism on predator and harvesting on prey Luis, Prisalo; Kamalia, Putri Zahra; Peter, Olumuyiwa James; Aldila, Dipo
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.30550

Abstract

The type of interaction between two different species in the same ecosystem plays an important role in the coexistence between these species. One type of interaction between species is predator-prey interaction. Several important factors are crucial to guarantee the existence of predator and prey in the same ecosystem, such as the carrying capacity of the ecosystem for the survival of prey, the intensity of predation, cannibalism in the predator population, and many other factors. External factors such as human intervention, such as harvesting, increase the complexity of the problem. Here in this article, we discuss a predator-prey model that takes predation and harvesting in prey populations into account. We implement a Non-Standard Finite Difference (NSFD) numerical scheme to solve our model due to it good performance on stability and approximation. Mathematical analysis on the existence and stability of equilibrium points from the discrete model was analyzed in detail. We implement a Nonstandard Finite Difference (NSFD) scheme to ensure numerical stability across various simulation scenarios. It is shown that NSFD has a better numerical stability compared to the standard numerical scheme like Euler or fourth-order Runge-Kutta method. From the sensitivity of autonomous simulation, we have shown that increases of cannibalism in predator populations will reduce predator populations, and as a result, the population of prey will increase due to the lack of number of predators. We also showed that increasing harvesting in prey populations may cause extinction in prey and predator populations. Furthermore, we have shown how periodic harvesting on prey populations may cause a critical condition on the existence of prey populations that takes a longer period to get recovered.
Mathematical Modeling on the Transmission Dynamics of Diphtheria with Optimal Control Strategies Oguntolu, Festus Abiodun; Peter, Olumuyiwa James; Omede, Benjamin Idoko; Balogun, Ghaniyyat Bolanle; Ajiboye, Aminat Olabisi; Panigoro, Hasan S.
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.29716

Abstract

Diphtheria is an acute bacterial infection caused by Corynebacterium diphtheriae, characterized by the formation of a pseudo-membrane in the throat, which can lead to airway obstruction and systemic complications. Despite the availability of effective vaccines, diphtheria remains a significant public health concern in many regions, particularly in areas with low immunization coverage. In this study, we formulated and rigorously analyzed a deter ministic epidemiological mathematical model to gain insight into the transmission dynamics of Diphtheria infection, incorporating the concentration of Corynebacterium Diphtheriae in the environment. The analysis of the model begins with the computation of the basic reproduction number and the examination of the local stability of the disease-free equilibrium using the Routh-Hurwitz criterion. An in-depth analysis of the model reveals that the model undergoes the phenomenon of backward bifurcation. This characteristic poses significant hurdles in effectively controlling Diph theria infection within the population. However, under the assumption of no re-infection of Diphtheria infection after recovery, the disease-free equilibrium point is globally asymptotically stable whenever the basic reproduction num ber is less than one. Furthermore, the sensitivity analysis of the basic reproduction number was carried out in order to determine the impact of each of the model basic parameters that contribute to the transmission of the disease. Utilizing the optimal control theory to effectively curb the spread of Diphtheria, We introduced two time dependent control measures, to mitigate the spread of Diphtheria. These time dependent control measures represent preventive actions, such as public enlightenment campaign to sensitize and educate the general public on the dynamics of Diph theria and proper personal hygiene which includes regular washing of hands to prevent susceptible individuals from acquiring Diphtheria, and environmental sanitation practices such as cleaning of surfaces and door handle to reduced the concentration of Corynebacterium diphtheriae in the environment. The results from the numerical simulations reveal that Diphtheria infection can successfully be controlled and mitigated within the population if we can increase the vaccination rate and the decay rate of Corynebacterium Diphtheriae in the environment, as well as properly and effectively implementing these optimal control measures simultaneously.
Analysis of Five-Year Malaria Prevalence at the Federal Teaching Hospital, Ido-Ekiti, Nigeria Mmaduakor, Chika; Ngwu, Benitho; Ojo-Lawal, Sherifat; Oluwafemi, Glory; Peter, Olumuyiwa James; Raso, Mario
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30958

Abstract

Malaria remains a major public health problem globally, with Nigeria accounting for approximately 27% of the global burden. Chronological analysis of malaria data is vital for evaluating the performance of malaria prevention programmes in Nigeria. Therefore, the objective of this study is to determine the malaria prevalence rate at the Federal Teaching Hospital, Ido-Ekiti (FETHI), over a five-year period. Data from 484 suspected malaria patients who visited the hospital between 2019 and 2023 were collected and analysed. Logistic regression was used to evaluate the relationship between positive blood film results and potential associated factors. Among all presumptive cases, 307 (63.4%) were female. The annual malaria prevalence ranged from 30.4% to 54.2%, with an overall prevalence of 42.32% (95% CI: 34.3%–54.4%). Two Plasmodium species were detected: Plasmodium falciparum (98 cases, 47.3%) and Plasmodium vivax (83 cases, 40.1%). A higher proportion of cases were recorded in December, January, and May (50%, 51.2%, and 51.4%, respectively). Patients who visited the hospital in January were twice as likely to be infected compared to those in April [OR: 2.29; 95% CI: 0.88–6.18; p = 0.037]. Males were half as likely to be infected as females [OR: 0.47; 95% CI: 0.30–0.72; p = 0.00066]. Malaria remains a significant concern in the studied location. Therefore, malaria control programmes need to be strengthened to reduce its impact.
NUMERICAL SOLUTION OF THE SEIR MODEL USING THE FOURTH-ORDER RUNGE-KUTTA METHOD TO PREDICT THE SPREAD OF HEPATITIS B DISEASE IN AMBON CITY Papalia, Anita; Lesnussa, Yopi Andry; Rijoly, Monalisa E.; Peter, Olumuyiwa James
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp2047-2056

Abstract

Hepatitis B is a dangerous type of hepatitis and has a high risk of death. This research aims to predict the spread of Hepatitis B in Ambon using the fourth-order Runge-Kutta method. The mathematical model for the spread of Hepatitis B takes the form of a system of differential equations that includes the variables Susceptible (S) namely the subpopulation that is susceptible to infection with the hepatitis B virus, Exposed (E), namely the subpopulation that is exposed to the hepatitis B virus when it comes into contact with the Infected (I) subpopulation, I, namely the subpopulation infected with hepatitis B and Recovered (R), namely the recovered subpopulation. The values ​​ , , , , , , , and are the parameter values ​​used to be solved numerically using the fourth order Runge Kutta method which was carried out in 20 iterations with step size h=1 using data from the Maluku Provincial Health Service and the Central Bureau of Statistics from 2013 to 2022. Hepatitis B is classified as a type of hepatitis disease that is dangerous and has a high risk of death. This study aimed to construct a model of the spread of Hepatitis B disease in Ambon City and solve the model using the fourth-order Runge-Kutta method. In the research results, it was obtained that subpopulation decreased significantly in the 20th year with a total of 299,239 people, for subpopulation increased in 18th year with a total of 4,309 people, and decreased in 20th year with a total of 4,298 people, for subpopulation subpopulation increased until 20th year with a total of 254 people, and for subpopulation subpopulation increased significantly in 20th year with a total of 10,776 people.
Co-Authors Abidemi, Afeez Adebisi, Ajimot F. Ajiboye, Aminat Olabisi Balogun, Ghaniyyat Bolanle Beay, Lazarus Kalvein Dipo Aldila Fatmawati Fatmawati Hasan S. Panigoro Ilwaru, Venn Yan Ishak Ishola, Christie Y. Kamalia, Putri Zahra Luis, Prisalo Mmaduakor, Chika Ngwu, Benitho Oguntolu, Festus Abiodun Ojo, Mayowa Micheal Ojo-Lawal, Sherifat Oluwafemi, Glory Omede, Benjamin Idoko Oseni, Wasiu A. Papalia, Anita Raso, Mario Rijoly, Monalisa E. Sahusilawane, Maria Engeline Uwaheren, Ohigweren A. Vynska Amalia Permadi Yopi Andry Lesnussa